Автоматический выбор регрессионной модели с оптимизированными гиперпараметрами
Данные предиктора и ответа, fitrauto автоматически пытается выбрать типы регрессионных моделей с различными значениями гиперпараметров. Функция использует байесовскую оптимизацию для выбора моделей и их значений гиперпараметров и вычисляет для каждой модели следующее: log ( 1 + valLoss), где valLoss - среднеквадратическая ошибка (MSE) перекрестной проверки. После завершения оптимизации fitrauto возвращает модель, обученную всему набору данных, которая, как ожидается, наилучшим образом предсказывает ответы на новые данные. Вы можете использовать predict и loss объектные функции возвращаемой модели для прогнозирования на новых данных и вычисления тестового набора MSE соответственно.
Использовать fitrauto когда вы не уверены, какие типы моделей лучше всего подходят для ваших данных. Сведения об альтернативных методах настройки гиперпараметров регрессионных моделей см. в разделе Альтернативная функциональность.
Mdl = fitrauto(Tbl,ResponseVarName)Mdl с настроенными гиперпараметрами. Стол Tbl содержит переменные предиктора и переменную ответа, где ResponseVarName - имя переменной ответа.
Mdl = fitrauto(___,Name,Value)HyperparameterOptimizationOptions аргумент пары имя-значение для указания способа выполнения байесовской оптимизации.
[ дополнительно возвращает Mdl,OptimizationResults] = fitrauto(___)OptimizationResults, a BayesianOptimization объект, содержащий результаты процесса выбора модели и настройки гиперпараметров.
Использовать fitrauto для автоматического выбора регрессионной модели с оптимизированными гиперпараметрами, заданными данными предиктора и ответа, сохраненными в таблице.
Загрузить данные
Загрузить carbig набор данных, содержащий замеры автомобилей, сделанные в 1970-х и начале 1980-х годов.
load carbigСоздание таблицы, содержащей переменные предиктора Acceleration, Displacementи так далее, а также переменная ответа MPG.
cars = table(Acceleration,Displacement,Horsepower, ...
Model_Year,Origin,Weight,MPG);Данные раздела
Разбейте данные на обучающие и тестовые наборы. Используйте приблизительно 80% наблюдений для процесса выбора модели и настройки гиперпараметров, а 20% наблюдений для проверки производительности конечной модели, возвращенной fitrauto. Использовать cvpartition для секционирования данных.
rng('default') % For reproducibility of the data partition c = cvpartition(length(MPG),'Holdout',0.2); trainingIdx = training(c); % Training set indices carsTrain = cars(trainingIdx,:); testIdx = test(c); % Test set indices carsTest = cars(testIdx,:);
Управляемый fitrauto
Передача данных обучения в fitrauto. По умолчанию fitrauto определяет подходящие типы моделей для попытки, использует байесовскую оптимизацию для поиска хороших значений гиперпараметров и возвращает обученную модель Mdl с наилучшей ожидаемой производительностью. Дополнительно, fitrauto предоставляет график оптимизации и итеративное отображение результатов оптимизации. Дополнительные сведения о том, как интерпретировать эти результаты, см. в разделе Подробный просмотр.
Ожидайте, что этот процесс займет некоторое время. Чтобы ускорить процесс оптимизации, попробуйте запустить оптимизацию параллельно, если у вас есть лицензия Parallel Computing Toolbox™. Для этого необходимо пройти 'HyperparameterOptimizationOptions',struct('UseParallel',true) кому fitrauto в качестве аргумента пары имя-значение.
Mdl = fitrauto(carsTrain,'MPG');Learner types to explore: ensemble, svm, tree Total iterations (MaxObjectiveEvaluations): 90 Total time (MaxTime): Inf |=========================================================================================================================================| | Iter | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |=========================================================================================================================================| | 1 | Best | 2.5161 | 1.4197 | 2.5161 | 2.5161 | tree | MinLeafSize: 6 |
| 2 | Accept | 4.1439 | 0.68799 | 2.5161 | 2.5161 | svm | BoxConstraint: 336.91 | | | | | | | | | KernelScale: 0.0018275 | | | | | | | | | Epsilon: 0.1074 |
| 3 | Accept | 4.144 | 5.5942 | 2.5161 | 2.5161 | ensemble | Method: Bag | | | | | | | | | NumLearningCycles: 257 | | | | | | | | | MinLeafSize: 156 |
| 4 | Accept | 3.1976 | 20.387 | 2.5161 | 2.5161 | svm | BoxConstraint: 0.033502 | | | | | | | | | KernelScale: 153.38 | | | | | | | | | Epsilon: 0.093672 |
| 5 | Best | 2.5041 | 0.13106 | 2.5041 | 2.5101 | tree | MinLeafSize: 5 |
| 6 | Best | 2.2096 | 7.0177 | 2.2096 | 2.5101 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 287 | | | | | | | | | MinLeafSize: 1 |
| 7 | Accept | 2.7182 | 0.085053 | 2.2096 | 2.5057 | tree | MinLeafSize: 1 |
| 8 | Accept | 17.207 | 23.312 | 2.2096 | 2.5057 | svm | BoxConstraint: 196.73 | | | | | | | | | KernelScale: 34.789 | | | | | | | | | Epsilon: 0.03716 |
| 9 | Accept | 4.1439 | 0.057226 | 2.2096 | 2.5057 | svm | BoxConstraint: 346.92 | | | | | | | | | KernelScale: 0.032493 | | | | | | | | | Epsilon: 0.23974 |
| 10 | Best | 2.1916 | 6.4368 | 2.1916 | 2.5057 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 278 | | | | | | | | | MinLeafSize: 13 |
|=========================================================================================================================================| | Iter | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |=========================================================================================================================================| | 11 | Accept | 2.8889 | 0.1325 | 2.1916 | 2.5057 | svm | BoxConstraint: 0.033068 | | | | | | | | | KernelScale: 585.38 | | | | | | | | | Epsilon: 4.6993 |
| 12 | Accept | 4.1439 | 0.06362 | 2.1916 | 2.5057 | svm | BoxConstraint: 48.997 | | | | | | | | | KernelScale: 0.0045904 | | | | | | | | | Epsilon: 18.085 |
| 13 | Accept | 4.1439 | 0.048941 | 2.1916 | 2.5057 | svm | BoxConstraint: 985.69 | | | | | | | | | KernelScale: 0.0010988 | | | | | | | | | Epsilon: 449.48 |
| 14 | Accept | 2.2844 | 6.7538 | 2.1916 | 2.4806 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 287 | | | | | | | | | MinLeafSize: 63 |
| 15 | Accept | 4.1439 | 0.054943 | 2.1916 | 2.4806 | svm | BoxConstraint: 0.010812 | | | | | | | | | KernelScale: 1.2015 | | | | | | | | | Epsilon: 0.034209 |
| 16 | Accept | 4.1439 | 0.055455 | 2.1916 | 2.4806 | svm | BoxConstraint: 0.0021787 | | | | | | | | | KernelScale: 0.018209 | | | | | | | | | Epsilon: 443.71 |
| 17 | Accept | 2.2075 | 6.7931 | 2.1916 | 2.1942 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 283 | | | | | | | | | MinLeafSize: 17 |
| 18 | Accept | 2.6056 | 0.08425 | 2.1916 | 2.1942 | tree | MinLeafSize: 2 |
| 19 | Accept | 2.6056 | 0.087135 | 2.1916 | 2.1942 | tree | MinLeafSize: 2 |
| 20 | Accept | 2.7182 | 0.062848 | 2.1916 | 2.1942 | tree | MinLeafSize: 1 |
|=========================================================================================================================================| | Iter | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |=========================================================================================================================================| | 21 | Accept | 2.2402 | 6.8909 | 2.1916 | 2.2011 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 282 | | | | | | | | | MinLeafSize: 2 |
| 22 | Accept | 2.6056 | 0.059067 | 2.1916 | 2.2011 | tree | MinLeafSize: 2 |
| 23 | Accept | 2.3016 | 4.8177 | 2.1916 | 2.1911 | ensemble | Method: Bag | | | | | | | | | NumLearningCycles: 202 | | | | | | | | | MinLeafSize: 9 |
| 24 | Accept | 4.1439 | 0.05258 | 2.1916 | 2.1911 | svm | BoxConstraint: 37.028 | | | | | | | | | KernelScale: 0.033731 | | | | | | | | | Epsilon: 0.2457 |
| 25 | Accept | 3.352 | 0.043391 | 2.1916 | 2.1911 | tree | MinLeafSize: 122 |
| 26 | Accept | 4.1439 | 0.062799 | 2.1916 | 2.1911 | svm | BoxConstraint: 0.01045 | | | | | | | | | KernelScale: 0.0024261 | | | | | | | | | Epsilon: 12.355 |
| 27 | Accept | 2.3188 | 5.1633 | 2.1916 | 2.1884 | ensemble | Method: Bag | | | | | | | | | NumLearningCycles: 212 | | | | | | | | | MinLeafSize: 2 |
| 28 | Accept | 2.4271 | 5.8444 | 2.1916 | 2.1908 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 247 | | | | | | | | | MinLeafSize: 83 |
| 29 | Accept | 2.6056 | 0.05574 | 2.1916 | 2.1908 | tree | MinLeafSize: 2 |
| 30 | Accept | 4.1439 | 0.054692 | 2.1916 | 2.1908 | svm | BoxConstraint: 2.1296 | | | | | | | | | KernelScale: 3.2623 | | | | | | | | | Epsilon: 599.62 |
|=========================================================================================================================================| | Iter | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |=========================================================================================================================================| | 31 | Accept | 2.5241 | 0.051793 | 2.1916 | 2.1908 | tree | MinLeafSize: 8 |
| 32 | Accept | 2.6443 | 5.2572 | 2.1916 | 2.1969 | ensemble | Method: Bag | | | | | | | | | NumLearningCycles: 229 | | | | | | | | | MinLeafSize: 52 |
| 33 | Accept | 2.2537 | 5.641 | 2.1916 | 2.1931 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 235 | | | | | | | | | MinLeafSize: 26 |
| 34 | Accept | 2.5448 | 0.053688 | 2.1916 | 2.1931 | tree | MinLeafSize: 19 |
| 35 | Accept | 2.4438 | 0.045817 | 2.1916 | 2.1931 | tree | MinLeafSize: 13 |
| 36 | Accept | 2.7182 | 0.062646 | 2.1916 | 2.1931 | tree | MinLeafSize: 1 |
| 37 | Accept | 2.4749 | 0.048072 | 2.1916 | 2.1931 | tree | MinLeafSize: 9 |
| 38 | Accept | 13.083 | 31.488 | 2.1916 | 2.1931 | svm | BoxConstraint: 5.2568 | | | | | | | | | KernelScale: 10.811 | | | | | | | | | Epsilon: 0.073361 |
| 39 | Accept | 2.2446 | 5.2866 | 2.1916 | 2.1952 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 214 | | | | | | | | | MinLeafSize: 4 |
| 40 | Accept | 3.0919 | 0.040315 | 2.1916 | 2.1952 | tree | MinLeafSize: 62 |
|=========================================================================================================================================| | Iter | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |=========================================================================================================================================| | 41 | Accept | 2.6335 | 6.4626 | 2.1916 | 2.1926 | ensemble | Method: Bag | | | | | | | | | NumLearningCycles: 280 | | | | | | | | | MinLeafSize: 45 |
| 42 | Accept | 4.1439 | 0.048186 | 2.1916 | 2.1926 | svm | BoxConstraint: 0.093799 | | | | | | | | | KernelScale: 0.0053728 | | | | | | | | | Epsilon: 17.332 |
| 43 | Accept | 2.8766 | 0.075435 | 2.1916 | 2.1926 | svm | BoxConstraint: 0.20553 | | | | | | | | | KernelScale: 880.29 | | | | | | | | | Epsilon: 4.5637 |
| 44 | Accept | 2.2402 | 5.6507 | 2.1916 | 2.1944 | ensemble | Method: LSBoost | | | | | | | | | NumLearningCycles: 233 | | | | | | | | | MinLeafSize: 2 |
| 45 | Accept | 2.4576 | 5.4632 | 2.1916 | 2.1928 | ensemble | Method: Bag | | | | | | | | | NumLearningCycles: 232 | | | | | | | | | MinLeafSize: 27 |
| 46 | Accept | 3.003 | 0.069043 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.0010563 | | | | | | | | | KernelScale: 527.21 | | | | | | | | | Epsilon: 0.010074 |
| 47 | Accept | 4.1439 | 0.05544 | 2.1916 | 2.1928 | svm | BoxConstraint: 1.6452 | | | | | | | | | KernelScale: 880.96 | | | | | | | | | Epsilon: 656.96 |
| 48 | Accept | 11.118 | 31.888 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.001029 | | | | | | | | | KernelScale: 25.502 | | | | | | | | | Epsilon: 0.22713 |
| 49 | Accept | 3.0019 | 0.064077 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.012054 | | | | | | | | | KernelScale: 976.62 | | | | | | | | | Epsilon: 0.013474 |
| 50 | Accept | 4.1439 | 0.069826 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.045381 | | | | | | | | | KernelScale: 0.030659 | | | | | | | | | Epsilon: 0.021441 |
|=========================================================================================================================================| | Iter | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |=========================================================================================================================================| | 51 | Accept | 4.1439 | 0.050005 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.090287 | | | | | | | | | KernelScale: 69.941 | | | | | | | | | Epsilon: 125.56 |
| 52 | Accept | 4.1439 | 0.054745 | 2.1916 | 2.1928 | svm | BoxConstraint: 285.67 | | | | | | | | | KernelScale: 0.14938 | | | | | | | | | Epsilon: 764.19 |
| 53 | Accept | 2.8779 | 0.11876 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.064002 | | | | | | | | | KernelScale: 969.91 | | | | | | | | | Epsilon: 0.46473 |
| 54 | Accept | 12.921 | 18.315 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.019899 | | | | | | | | | KernelScale: 50.528 | | | | | | | | | Epsilon: 0.0091628 |
| 55 | Accept | 2.9117 | 0.076534 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.028436 | | | | | | | | | KernelScale: 919.02 | | | | | | | | | Epsilon: 1.2395 |
| 56 | Accept | 3.0276 | 0.064801 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.0073097 | | | | | | | | | KernelScale: 898.72 | | | | | | | | | Epsilon: 0.088715 |
| 57 | Accept | 7.1555 | 20.87 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.07913 | | | | | | | | | KernelScale: 100.43 | | | | | | | | | Epsilon: 0.78937 |
| 58 | Accept | 2.9075 | 0.077548 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.03913 | | | | | | | | | KernelScale: 956.28 | | | | | | | | | Epsilon: 1.1315 |
| 59 | Accept | 2.9168 | 0.068648 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.033583 | | | | | | | | | KernelScale: 973.75 | | | | | | | | | Epsilon: 2.1404 |
| 60 | Accept | 4.1439 | 0.053635 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.1278 | | | | | | | | | KernelScale: 899.12 | | | | | | | | | Epsilon: 36.993 |
|=========================================================================================================================================| | Iter | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |=========================================================================================================================================| | 61 | Accept | 2.9456 | 0.073895 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.022705 | | | | | | | | | KernelScale: 995.04 | | | | | | | | | Epsilon: 0.21977 |
| 62 | Accept | 4.1439 | 0.04979 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.0047868 | | | | | | | | | KernelScale: 0.1518 | | | | | | | | | Epsilon: 0.042601 |
| 63 | Accept | 2.9095 | 0.065115 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.033402 | | | | | | | | | KernelScale: 989.34 | | | | | | | | | Epsilon: 0.3073 |
| 64 | Accept | 4.1439 | 0.065248 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.056303 | | | | | | | | | KernelScale: 0.29988 | | | | | | | | | Epsilon: 0.10313 |
| 65 | Accept | 4.1439 | 0.050181 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.0040769 | | | | | | | | | KernelScale: 238.59 | | | | | | | | | Epsilon: 32.573 |
| 66 | Accept | 2.6802 | 2.1221 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.11739 | | | | | | | | | KernelScale: 555.21 | | | | | | | | | Epsilon: 0.048956 |
| 67 | Accept | 4.1439 | 0.055315 | 2.1916 | 2.1928 | svm | BoxConstraint: 772.51 | | | | | | | | | KernelScale: 0.016887 | | | | | | | | | Epsilon: 72.705 |
| 68 | Accept | 4.1439 | 0.063152 | 2.1916 | 2.1928 | svm | BoxConstraint: 63.153 | | | | | | | | | KernelScale: 0.0080065 | | | | | | | | | Epsilon: 481.39 |
| 69 | Accept | 4.1439 | 0.054083 | 2.1916 | 2.1928 | svm | BoxConstraint: 4.117 | | | | | | | | | KernelScale: 73.496 | | | | | | | | | Epsilon: 121.74 |
| 70 | Accept | 4.1439 | 0.05377 | 2.1916 | 2.1928 | svm | BoxConstraint: 30.398 | | | | | | | | | KernelScale: 0.12159 | | | | | | | | | Epsilon: 64.06 |
|=========================================================================================================================================| | Iter | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |=========================================================================================================================================| | 71 | Accept | 4.1439 | 0.053553 | 2.1916 | 2.1928 | svm | BoxConstraint: 3.9304 | | | | | | | | | KernelScale: 871.88 | | | | | | | | | Epsilon: 23.7 |
| 72 | Accept | 4.1439 | 0.050525 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.031734 | | | | | | | | | KernelScale: 0.28247 | | | | | | | | | Epsilon: 0.0097239 |
| 73 | Accept | 4.1439 | 0.068567 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.021528 | | | | | | | | | KernelScale: 0.001858 | | | | | | | | | Epsilon: 283.71 |
| 74 | Accept | 4.1439 | 0.055336 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.024702 | | | | | | | | | KernelScale: 0.055101 | | | | | | | | | Epsilon: 84.374 |
| 75 | Accept | 2.8707 | 0.095257 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.070484 | | | | | | | | | KernelScale: 928.16 | | | | | | | | | Epsilon: 0.11681 |
| 76 | Accept | 4.1439 | 0.059476 | 2.1916 | 2.1928 | svm | BoxConstraint: 636.13 | | | | | | | | | KernelScale: 0.0020368 | | | | | | | | | Epsilon: 2.0625 |
| 77 | Accept | 2.8682 | 0.10867 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.059284 | | | | | | | | | KernelScale: 888.99 | | | | | | | | | Epsilon: 0.1389 |
| 78 | Accept | 2.7111 | 0.59286 | 2.1916 | 2.1928 | svm | BoxConstraint: 2.4776 | | | | | | | | | KernelScale: 998.2 | | | | | | | | | Epsilon: 1.5291 |
| 79 | Accept | 2.7625 | 0.45668 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.91288 | | | | | | | | | KernelScale: 996.35 | | | | | | | | | Epsilon: 0.16968 |
| 80 | Accept | 3.2211 | 0.058812 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.0011498 | | | | | | | | | KernelScale: 989.38 | | | | | | | | | Epsilon: 0.0091368 |
|=========================================================================================================================================| | Iter | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |=========================================================================================================================================| | 81 | Accept | 4.1439 | 0.05754 | 2.1916 | 2.1928 | svm | BoxConstraint: 26.543 | | | | | | | | | KernelScale: 0.0016089 | | | | | | | | | Epsilon: 0.68659 |
| 82 | Accept | 4.1439 | 0.055356 | 2.1916 | 2.1928 | svm | BoxConstraint: 129.11 | | | | | | | | | KernelScale: 0.044504 | | | | | | | | | Epsilon: 3.7911 |
| 83 | Accept | 2.7643 | 0.51644 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.82852 | | | | | | | | | KernelScale: 990.02 | | | | | | | | | Epsilon: 0.013169 |
| 84 | Accept | 4.1439 | 0.05615 | 2.1916 | 2.1928 | svm | BoxConstraint: 53.003 | | | | | | | | | KernelScale: 3.9941 | | | | | | | | | Epsilon: 318.78 |
| 85 | Accept | 4.1439 | 0.054645 | 2.1916 | 2.1928 | svm | BoxConstraint: 10.848 | | | | | | | | | KernelScale: 0.2138 | | | | | | | | | Epsilon: 876.72 |
| 86 | Accept | 2.8797 | 0.077707 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.063788 | | | | | | | | | KernelScale: 999.56 | | | | | | | | | Epsilon: 0.24966 |
| 87 | Accept | 4.1439 | 0.056472 | 2.1916 | 2.1928 | svm | BoxConstraint: 29.921 | | | | | | | | | KernelScale: 300.51 | | | | | | | | | Epsilon: 872.64 |
| 88 | Accept | 4.1439 | 0.053269 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.5701 | | | | | | | | | KernelScale: 0.020421 | | | | | | | | | Epsilon: 282.76 |
| 89 | Accept | 4.1439 | 0.054778 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.60472 | | | | | | | | | KernelScale: 0.0052641 | | | | | | | | | Epsilon: 0.11831 |
| 90 | Accept | 2.8676 | 0.097394 | 2.1916 | 2.1928 | svm | BoxConstraint: 0.11411 | | | | | | | | | KernelScale: 977.02 | | | | | | | | | Epsilon: 0.090725 |
__________________________________________________________ Optimization completed. Total iterations: 90 Total elapsed time: 589.6892 seconds Total time for training and validation: 245.2123 seconds Best observed learner is an ensemble model with: Method: LSBoost NumLearningCycles: 278 MinLeafSize: 13 Observed log(1 + valLoss): 2.1916 Time for training and validation: 6.4368 seconds Best estimated learner (returned model) is an ensemble model with: Method: LSBoost NumLearningCycles: 278 MinLeafSize: 13 Estimated log(1 + valLoss): 2.1928 Estimated time for training and validation: 5.8977 seconds Documentation for fitrauto display
Последняя модель, возвращенная fitrauto соответствует лучшему предполагаемому ученику. Перед возвращением модели функция переобучает её, используя все данные обучения (carsTrain), перечисленные Learner тип (или модель) и отображаемые значения гиперпараметров.
Оценка производительности тестового набора
Оцените производительность модели в тестовом наборе. testError основан на среднеквадратичной ошибке (MSE) тестового набора. Меньшие значения MSE указывают на лучшую производительность.
testMSE = loss(Mdl,carsTest,'MPG');
testError = log(1 + testMSE)testError = 2.3194
Использовать fitrauto для автоматического выбора регрессионной модели с оптимизированными гиперпараметрами, заданными данными предиктора и ответа, хранящимися в отдельных переменных.
Загрузить данные
Загрузить carbig набор данных, содержащий замеры автомобилей, сделанные в 1970-х и начале 1980-х годов.
load carbigСоздание матрицы X содержащие переменные предиктора Acceleration, Cylindersи так далее. Сохранить переменную ответа MPG в переменной Y.
X = [Acceleration Cylinders Displacement Weight]; Y = MPG;
Создайте переменную, указывающую, какие предикторы являются категориальными. Cylinders является единственной категориальной переменной в X.
categoricalVars = [false true false false];
Данные раздела
Разбейте данные на обучающие и тестовые наборы. Используйте приблизительно 80% наблюдений для процесса выбора модели и настройки гиперпараметров, а 20% наблюдений для проверки производительности конечной модели, возвращенной fitrauto. Использовать cvpartition для секционирования данных.
rng('default') % For reproducibility of the partition c = cvpartition(length(Y),'Holdout',0.20); trainingIdx = training(c); % Indices for the training set XTrain = X(trainingIdx,:); YTrain = Y(trainingIdx); testIdx = test(c); % Indices for the test set XTest = X(testIdx,:); YTest = Y(testIdx);
Управляемый fitrauto
Передача данных обучения в fitrauto. По умолчанию fitrauto определяет подходящие типы моделей (или обучающихся) для попытки, использует байесовскую оптимизацию для поиска хороших значений гиперпараметров для этих моделей и возвращает обученную модель Mdl с наилучшей ожидаемой производительностью. Укажите категориальные предикторы и запустите оптимизацию параллельно (требуется Toolbox™ параллельных вычислений). Возврат второго выходного сигнала OptimizationResults содержит подробности байесовской оптимизации.
Ожидайте, что этот процесс займет некоторое время. По умолчанию fitrauto предоставляет график оптимизации и итеративное отображение результатов оптимизации. Дополнительные сведения о том, как интерпретировать эти результаты, см. в разделе Подробный просмотр.
options = struct('UseParallel',true); [Mdl,OptimizationResults] = fitrauto(XTrain,YTrain, ... 'CategoricalPredictors',categoricalVars, ... 'HyperparameterOptimizationOptions',options);
Starting parallel pool (parpool) using the 'local' profile ... Connected to the parallel pool (number of workers: 6). Copying objective function to workers... Done copying objective function to workers.
Learner types to explore: ensemble, svm, tree Total iterations (MaxObjectiveEvaluations): 90 Total time (MaxTime): Inf
|===================================================================================================================================================| | Iter | Active | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 1 | 5 | Best | 3.0205 | 1.7491 | 3.0205 | 3.0329 | tree | MinLeafSize: 6 | | 2 | 5 | Accept | 3.0453 | 1.6641 | 3.0205 | 3.0329 | tree | MinLeafSize: 5 |
| 3 | 4 | Accept | 4.143 | 2.6491 | 3.0205 | 3.0329 | svm | BoxConstraint: 336.91 | | | | | | | | | | KernelScale: 0.0018275 | | | | | | | | | | Epsilon: 0.1074 | | 4 | 4 | Accept | 4.1434 | 7.5491 | 3.0205 | 3.0329 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 257 | | | | | | | | | | MinLeafSize: 156 |
| 5 | 3 | Best | 2.9188 | 8.6194 | 2.9188 | 3.0329 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 287 | | | | | | | | | | MinLeafSize: 1 | | 6 | 3 | Accept | 4.143 | 0.83485 | 2.9188 | 3.0329 | svm | BoxConstraint: 346.92 | | | | | | | | | | KernelScale: 0.032493 | | | | | | | | | | Epsilon: 0.23974 |
| 7 | 6 | Accept | 2.9275 | 0.19147 | 2.9188 | 2.9276 | svm | BoxConstraint: 0.033068 | | | | | | | | | | KernelScale: 585.38 | | | | | | | | | | Epsilon: 4.6993 |
| 8 | 4 | Accept | 4.143 | 0.09353 | 2.9188 | 2.9276 | svm | BoxConstraint: 985.69 | | | | | | | | | | KernelScale: 0.0010988 | | | | | | | | | | Epsilon: 449.48 | | 9 | 4 | Accept | 4.143 | 0.62222 | 2.9188 | 2.9276 | svm | BoxConstraint: 0.04588 | | | | | | | | | | KernelScale: 0.33917 | | | | | | | | | | Epsilon: 0.073755 | | 10 | 4 | Accept | 3.0205 | 0.21301 | 2.9188 | 2.9276 | tree | MinLeafSize: 6 |
|===================================================================================================================================================| | Iter | Active | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 11 | 6 | Best | 2.9167 | 7.3685 | 2.9167 | 2.9276 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 287 | | | | | | | | | | MinLeafSize: 63 |
| 12 | 4 | Accept | 3.6673 | 22.826 | 2.8696 | 2.8697 | svm | BoxConstraint: 0.033502 | | | | | | | | | | KernelScale: 153.38 | | | | | | | | | | Epsilon: 0.093672 | | 13 | 4 | Best | 2.8696 | 8.0371 | 2.8696 | 2.8697 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 283 | | | | | | | | | | MinLeafSize: 17 | | 14 | 4 | Accept | 2.8696 | 7.6155 | 2.8696 | 2.8697 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 283 | | | | | | | | | | MinLeafSize: 17 |
| 15 | 3 | Accept | 2.8696 | 8.2039 | 2.8696 | 2.8697 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 283 | | | | | | | | | | MinLeafSize: 17 | | 16 | 3 | Accept | 3.1971 | 0.1933 | 2.8696 | 2.8697 | tree | MinLeafSize: 2 |
| 17 | 6 | Accept | 3.0139 | 0.12079 | 2.8696 | 2.8697 | tree | MinLeafSize: 34 |
| 18 | 5 | Accept | 4.143 | 0.23444 | 2.8696 | 2.8697 | svm | BoxConstraint: 0.0023916 | | | | | | | | | | KernelScale: 0.0049969 | | | | | | | | | | Epsilon: 3.0552 | | 19 | 5 | Accept | 3.3225 | 0.19712 | 2.8696 | 2.8697 | tree | MinLeafSize: 122 |
| 20 | 3 | Accept | 2.8717 | 5.5602 | 2.8217 | 2.8697 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 282 | | | | | | | | | | MinLeafSize: 2 | |===================================================================================================================================================| | Iter | Active | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 21 | 3 | Best | 2.8217 | 4.2702 | 2.8217 | 2.8697 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 202 | | | | | | | | | | MinLeafSize: 9 | | 22 | 3 | Accept | 4.143 | 0.11628 | 2.8217 | 2.8697 | svm | BoxConstraint: 37.028 | | | | | | | | | | KernelScale: 0.033731 | | | | | | | | | | Epsilon: 0.2457 |
| 23 | 6 | Accept | 4.143 | 0.067367 | 2.8217 | 2.8697 | svm | BoxConstraint: 0.01045 | | | | | | | | | | KernelScale: 0.0024261 | | | | | | | | | | Epsilon: 12.355 |
| 24 | 5 | Accept | 3.1971 | 0.094668 | 2.8217 | 2.8697 | tree | MinLeafSize: 2 | | 25 | 5 | Accept | 4.143 | 0.10279 | 2.8217 | 2.8697 | svm | BoxConstraint: 308.5 | | | | | | | | | | KernelScale: 0.015174 | | | | | | | | | | Epsilon: 0.53501 |
| 26 | 5 | Accept | 4.143 | 0.07812 | 2.8217 | 2.8697 | svm | BoxConstraint: 2.1296 | | | | | | | | | | KernelScale: 3.2623 | | | | | | | | | | Epsilon: 599.62 |
| 27 | 6 | Accept | 11.41 | 32.991 | 2.8217 | 2.8697 | svm | BoxConstraint: 0.0054638 | | | | | | | | | | KernelScale: 45.011 | | | | | | | | | | Epsilon: 5.0385 |
| 28 | 6 | Accept | 2.8657 | 5.3498 | 2.8217 | 2.8221 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 229 | | | | | | | | | | MinLeafSize: 52 |
| 29 | 3 | Accept | 2.8689 | 6.3959 | 2.8217 | 2.8221 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 235 | | | | | | | | | | MinLeafSize: 26 | | 30 | 3 | Accept | 2.8689 | 5.5649 | 2.8217 | 2.8221 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 235 | | | | | | | | | | MinLeafSize: 26 | |===================================================================================================================================================| | Iter | Active | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 31 | 3 | Accept | 2.9197 | 0.043492 | 2.8217 | 2.8221 | tree | MinLeafSize: 19 | | 32 | 3 | Accept | 2.9403 | 0.050907 | 2.8217 | 2.8221 | tree | MinLeafSize: 13 |
| 33 | 6 | Accept | 4.143 | 0.1117 | 2.8217 | 2.8221 | svm | BoxConstraint: 0.0013002 | | | | | | | | | | KernelScale: 365.07 | | | | | | | | | | Epsilon: 533.39 |
| 34 | 5 | Accept | 4.1924 | 16.905 | 2.8217 | 2.8221 | svm | BoxConstraint: 0.0057208 | | | | | | | | | | KernelScale: 143.79 | | | | | | | | | | Epsilon: 4.0917 | | 35 | 5 | Accept | 2.9804 | 0.16413 | 2.8217 | 2.8221 | tree | MinLeafSize: 8 |
| 36 | 4 | Accept | 2.8842 | 4.4972 | 2.8217 | 2.8221 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 214 | | | | | | | | | | MinLeafSize: 4 | | 37 | 4 | Accept | 3.112 | 0.40292 | 2.8217 | 2.8221 | tree | MinLeafSize: 62 |
| 38 | 3 | Accept | 2.8686 | 5.942 | 2.8217 | 2.8221 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 285 | | | | | | | | | | MinLeafSize: 45 | | 39 | 3 | Accept | 4.143 | 0.048389 | 2.8217 | 2.8221 | svm | BoxConstraint: 0.093799 | | | | | | | | | | KernelScale: 0.0053728 | | | | | | | | | | Epsilon: 17.332 |
| 40 | 6 | Accept | 2.9487 | 0.053171 | 2.8217 | 2.8221 | tree | MinLeafSize: 27 |
|===================================================================================================================================================| | Iter | Active | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 41 | 3 | Accept | 12.196 | 29.49 | 2.8217 | 2.8221 | svm | BoxConstraint: 86.083 | | | | | | | | | | KernelScale: 52.727 | | | | | | | | | | Epsilon: 8.3179 | | 42 | 3 | Accept | 2.8717 | 4.5788 | 2.8217 | 2.8221 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 233 | | | | | | | | | | MinLeafSize: 2 | | 43 | 3 | Accept | 2.9093 | 0.24973 | 2.8217 | 2.8221 | svm | BoxConstraint: 0.034974 | | | | | | | | | | KernelScale: 588.77 | | | | | | | | | | Epsilon: 3.8683 | | 44 | 3 | Accept | 2.9804 | 0.18263 | 2.8217 | 2.8221 | tree | MinLeafSize: 8 |
| 45 | 6 | Accept | 4.143 | 0.10875 | 2.8217 | 2.8221 | svm | BoxConstraint: 0.084355 | | | | | | | | | | KernelScale: 0.052988 | | | | | | | | | | Epsilon: 76.921 |
| 46 | 5 | Accept | 2.8478 | 4.7428 | 2.8217 | 2.8221 | ensemble | Method: LSBoost | | | | | | | | | | NumLearningCycles: 229 | | | | | | | | | | MinLeafSize: 8 | | 47 | 5 | Accept | 4.143 | 1.2887 | 2.8217 | 2.8221 | svm | BoxConstraint: 0.0036358 | | | | | | | | | | KernelScale: 4.7627 | | | | | | | | | | Epsilon: 20.208 |
| 48 | 4 | Accept | 3.2214 | 16.267 | 2.8217 | 2.8221 | svm | BoxConstraint: 0.069952 | | | | | | | | | | KernelScale: 207.68 | | | | | | | | | | Epsilon: 0.092526 | | 49 | 4 | Accept | 2.924 | 0.18896 | 2.8217 | 2.8221 | svm | BoxConstraint: 0.0095751 | | | | | | | | | | KernelScale: 358.95 | | | | | | | | | | Epsilon: 4.7526 |
| 50 | 3 | Accept | 3.1542 | 15.88 | 2.8217 | 2.8221 | svm | BoxConstraint: 0.028095 | | | | | | | | | | KernelScale: 184.52 | | | | | | | | | | Epsilon: 0.09847 | |===================================================================================================================================================| | Iter | Active | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 51 | 3 | Accept | 2.9143 | 3.0279 | 2.8217 | 2.8221 | svm | BoxConstraint: 0.0033005 | | | | | | | | | | KernelScale: 252.81 | | | | | | | | | | Epsilon: 2.6159 |
| 52 | 6 | Accept | 10.06 | 18.169 | 2.8217 | 2.8221 | svm | BoxConstraint: 0.043122 | | | | | | | | | | KernelScale: 74.674 | | | | | | | | | | Epsilon: 0.071781 |
| 53 | 2 | Accept | 2.8989 | 7.2493 | 2.8217 | 2.8221 | svm | BoxConstraint: 0.014817 | | | | | | | | | | KernelScale: 247.68 | | | | | | | | | | Epsilon: 2.5942 | | 54 | 2 | Accept | 2.9049 | 0.55744 | 2.8217 | 2.8221 | svm | BoxConstraint: 0.033022 | | | | | | | | | | KernelScale: 505.18 | | | | | | | | | | Epsilon: 0.1266 | | 55 | 2 | Accept | 2.9804 | 0.066427 | 2.8217 | 2.8221 | tree | MinLeafSize: 8 | | 56 | 2 | Accept | 2.9032 | 0.17339 | 2.8217 | 2.8221 | tree | MinLeafSize: 17 | | 57 | 2 | Accept | 4.143 | 0.058535 | 2.8217 | 2.8221 | svm | BoxConstraint: 0.0011341 | | | | | | | | | | KernelScale: 0.0017464 | | | | | | | | | | Epsilon: 0.012532 |
| 58 | 6 | Accept | 2.9268 | 0.13315 | 2.8217 | 2.8221 | svm | BoxConstraint: 0.0042653 | | | | | | | | | | KernelScale: 319.4 | | | | | | | | | | Epsilon: 4.5985 |
| 59 | 4 | Accept | 2.9081 | 1.8508 | 2.8217 | 2.8227 | svm | BoxConstraint: 0.0012679 | | | | | | | | | | KernelScale: 229.31 | | | | | | | | | | Epsilon: 0.075286 | | 60 | 4 | Accept | 4.143 | 0.059851 | 2.8217 | 2.8227 | svm | BoxConstraint: 275.76 | | | | | | | | | | KernelScale: 0.034549 | | | | | | | | | | Epsilon: 6.2312 | |===================================================================================================================================================| | Iter | Active | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 61 | 4 | Accept | 2.8335 | 4.6933 | 2.8217 | 2.8227 | ensemble | Method: Bag | | | | | | | | | | NumLearningCycles: 219 | | | | | | | | | | MinLeafSize: 26 |
| 62 | 5 | Accept | 2.9049 | 1.902 | 2.8217 | 2.8227 | svm | BoxConstraint: 0.0071219 | | | | | | | | | | KernelScale: 278.65 | | | | | | | | | | Epsilon: 2.7464 |
| 63 | 3 | Accept | 2.8816 | 15.271 | 2.8217 | 2.8227 | svm | BoxConstraint: 0.044779 | | | | | | | | | | KernelScale: 253.31 | | | | | | | | | | Epsilon: 0.15109 | | 64 | 3 | Accept | 2.8773 | 9.1951 | 2.8217 | 2.8227 | svm | BoxConstraint: 0.042581 | | | | | | | | | | KernelScale: 336.99 | | | | | | | | | | Epsilon: 0.072146 | | 65 | 3 | Accept | 2.9573 | 3.597 | 2.8217 | 2.8227 | svm | BoxConstraint: 0.035397 | | | | | | | | | | KernelScale: 251.22 | | | | | | | | | | Epsilon: 5.8103 |
| 66 | 6 | Accept | 2.9045 | 0.8479 | 2.8217 | 2.8227 | svm | BoxConstraint: 0.0017256 | | | | | | | | | | KernelScale: 280.49 | | | | | | | | | | Epsilon: 0.17061 |
| 67 | 5 | Accept | 3.1507 | 0.089958 | 2.8217 | 2.8227 | tree | MinLeafSize: 3 | | 68 | 5 | Accept | 3.1971 | 0.14914 | 2.8217 | 2.8227 | tree | MinLeafSize: 2 |
| 69 | 5 | Accept | 4.143 | 30.354 | 2.8217 | 2.8227 | svm | BoxConstraint: 1.3468 | | | | | | | | | | KernelScale: 9.6762 | | | | | | | | | | Epsilon: 0.023868 |
| 70 | 5 | Accept | 2.9037 | 1.2103 | 2.8217 | 2.8227 | svm | BoxConstraint: 0.0030905 | | | | | | | | | | KernelScale: 288.83 | | | | | | | | | | Epsilon: 0.089541 |
|===================================================================================================================================================| | Iter | Active | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 71 | 4 | Accept | 6.6283 | 17.347 | 2.8217 | 2.8227 | svm | BoxConstraint: 0.0017058 | | | | | | | | | | KernelScale: 104.21 | | | | | | | | | | Epsilon: 0.065687 | | 72 | 4 | Accept | 2.9655 | 15.866 | 2.8217 | 2.8227 | svm | BoxConstraint: 16.694 | | | | | | | | | | KernelScale: 563.25 | | | | | | | | | | Epsilon: 0.82854 |
| 73 | 4 | Accept | 3.0653 | 0.064937 | 2.8217 | 2.8227 | svm | BoxConstraint: 0.0014988 | | | | | | | | | | KernelScale: 637.21 | | | | | | | | | | Epsilon: 0.082183 |
| 74 | 2 | Accept | 5.9041 | 19.341 | 2.8217 | 2.8227 | svm | BoxConstraint: 0.0015248 | | | | | | | | | | KernelScale: 115.07 | | | | | | | | | | Epsilon: 0.14178 | | 75 | 2 | Accept | 2.874 | 14.077 | 2.8217 | 2.8227 | svm | BoxConstraint: 0.049938 | | | | | | | | | | KernelScale: 249.2 | | | | | | | | | | Epsilon: 2.3027 | | 76 | 2 | Accept | 2.9116 | 0.1932 | 2.8217 | 2.8227 | svm | BoxConstraint: 0.0015667 | | | | | | | | | | KernelScale: 364.11 | | | | | | | | | | Epsilon: 0.046357 |
| 77 | 6 | Accept | 2.9266 | 0.089378 | 2.8217 | 2.8203 | svm | BoxConstraint: 0.008711 | | | | | | | | | | KernelScale: 689.75 | | | | | | | | | | Epsilon: 0.11038 |
| 78 | 3 | Accept | 2.9134 | 0.2501 | 2.8217 | 2.7031 | svm | BoxConstraint: 0.0013447 | | | | | | | | | | KernelScale: 362.68 | | | | | | | | | | Epsilon: 0.096474 | | 79 | 3 | Accept | 4.143 | 0.086465 | 2.8217 | 2.7031 | svm | BoxConstraint: 37.006 | | | | | | | | | | KernelScale: 0.031201 | | | | | | | | | | Epsilon: 8.5325 | | 80 | 3 | Accept | 2.9804 | 0.070321 | 2.8217 | 2.7031 | tree | MinLeafSize: 8 | |===================================================================================================================================================| | Iter | Active | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 81 | 3 | Accept | 4.143 | 0.057551 | 2.8217 | 2.7031 | svm | BoxConstraint: 8.2928 | | | | | | | | | | KernelScale: 0.22318 | | | | | | | | | | Epsilon: 0.35272 |
| 82 | 6 | Accept | 2.905 | 0.35685 | 2.8217 | 2.6899 | svm | BoxConstraint: 0.0049863 | | | | | | | | | | KernelScale: 405.18 | | | | | | | | | | Epsilon: 0.20248 |
| 83 | 4 | Accept | 4.143 | 0.057428 | 2.8217 | 2.6899 | svm | BoxConstraint: 0.0035019 | | | | | | | | | | KernelScale: 10.124 | | | | | | | | | | Epsilon: 22.114 | | 84 | 4 | Accept | 2.9968 | 0.053485 | 2.8217 | 2.6899 | tree | MinLeafSize: 31 | | 85 | 4 | Accept | 2.9487 | 0.067551 | 2.8217 | 2.6899 | tree | MinLeafSize: 27 |
| 86 | 2 | Accept | 11.192 | 19.605 | 2.8217 | 2.7382 | svm | BoxConstraint: 86.675 | | | | | | | | | | KernelScale: 92.212 | | | | | | | | | | Epsilon: 2.4057 | | 87 | 2 | Accept | 2.8848 | 6.0635 | 2.8217 | 2.7382 | svm | BoxConstraint: 0.015422 | | | | | | | | | | KernelScale: 295.63 | | | | | | | | | | Epsilon: 0.10658 | | 88 | 2 | Accept | 2.8919 | 2.8002 | 2.8217 | 2.7382 | svm | BoxConstraint: 0.013027 | | | | | | | | | | KernelScale: 316.74 | | | | | | | | | | Epsilon: 0.1048 |
| 89 | 6 | Accept | 2.9712 | 0.073966 | 2.8217 | 2.7363 | svm | BoxConstraint: 0.00197 | | | | | | | | | | KernelScale: 560.31 | | | | | | | | | | Epsilon: 0.42707 |
| 90 | 5 | Accept | 3.0045 | 0.1149 | 2.8217 | 2.7363 | tree | MinLeafSize: 45 | |===================================================================================================================================================| | Iter | Active | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 91 | 5 | Accept | 3.031 | 0.041383 | 2.8217 | 2.7363 | tree | MinLeafSize: 61 |
__________________________________________________________ Optimization completed. Total iterations: 91 Total elapsed time: 201.923 seconds Total time for training and validation: 436.1019 seconds Best observed learner is an ensemble model with: Method: Bag NumLearningCycles: 202 MinLeafSize: 9 Observed log(1 + valLoss): 2.8217 Time for training and validation: 4.2702 seconds Best estimated learner (returned model) is an svm model with: BoxConstraint: 0.0013447 KernelScale: 362.68 Epsilon: 0.096474 Estimated log(1 + valLoss): 2.7363 Estimated time for training and validation: 0.29514 seconds Documentation for fitrauto display
Последняя модель, возвращенная fitrauto соответствует лучшему предполагаемому ученику. Перед возвращением модели функция переобучает её, используя все данные обучения (XTrain и YTrain), перечисленные Learner тип (или модель) и отображаемые значения гиперпараметров.
Оценка производительности тестового набора
Оцените производительность модели в тестовом наборе. testError основан на среднеквадратичной ошибке (MSE) тестового набора. Меньшие значения MSE указывают на лучшую производительность.
testMSE = loss(Mdl,XTest,YTest); testError = log(1 + testMSE)
testError = 2.9873
Использовать fitrauto для автоматического выбора регрессионной модели с оптимизированными гиперпараметрами, заданными данными предиктора и ответа, сохраненными в таблице. Сравнение производительности результирующей регрессионной модели с производительностью простой линейной регрессионной модели, созданной с помощью fitlm.
Загрузка и разбиение данных
Загрузить carbig набор данных, содержащий замеры автомобилей, сделанные в 1970-х и начале 1980-х годов. Преобразовать Cylinders переменной к categorical переменная. Создание таблицы, содержащей переменные предиктора Acceleration, Cylinders, Displacementи так далее, а также переменная ответа MPG.
load carbig Cylinders = categorical(Cylinders); cars = table(Acceleration,Cylinders,Displacement, ... Horsepower,Model_Year,Origin,Weight,MPG);
Разбейте данные на обучающие и тестовые наборы. Используйте приблизительно 80% наблюдений для обучения и 20% наблюдений для тестирования. Использовать cvpartition для секционирования данных.
rng('default') % For reproducibility of the data partition c = cvpartition(length(MPG),'Holdout',0.2); trainingIdx = training(c); % Training set indices carsTrain = cars(trainingIdx,:); testIdx = test(c); % Test set indices carsTest = cars(testIdx,:);
Управляемый fitrauto
Передача данных обучения в fitrauto. По умолчанию fitrauto определяет подходящие типы моделей для попытки, использует байесовскую оптимизацию для поиска хороших значений гиперпараметров и возвращает обученную модель autoMdl с наилучшей ожидаемой производительностью. Укажите, следует ли оптимизировать все оптимизируемые гиперпараметры и выполнять оптимизацию параллельно (требуется Toolbox™ параллельных вычислений).
Ожидайте, что этот процесс займет некоторое время. По умолчанию fitrauto предоставляет график оптимизации и итеративное отображение результатов оптимизации. Дополнительные сведения о том, как интерпретировать эти результаты, см. в разделе Подробный просмотр.
options = struct('UseParallel',true); autoMdl = fitrauto(carsTrain,'MPG','OptimizeHyperparameters','all', ... 'HyperparameterOptimizationOptions',options);
Starting parallel pool (parpool) using the 'local' profile ... Connected to the parallel pool (number of workers: 6). Copying objective function to workers... Done copying objective function to workers. Learner types to explore: ensemble, svm, tree Total iterations (MaxObjectiveEvaluations): 90 Total time (MaxTime): Inf |===================================================================================================================================================| | Iter | Active | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 1 | 4 | Accept | 3.5168 | 2.3522 | 2.6193 | 2.6197 | tree | MinLeafSize: 38 | | | | | | | | | | MaxNumSplits: 2 | | | | | | | | | | NumVariablesToSample: 1 | | 2 | 4 | Accept | 2.6633 | 2.3211 | 2.6193 | 2.6197 | tree | MinLeafSize: 1 | | | | | | | | | | MaxNumSplits: 44 | | | | | | | | | | NumVariablesToSample: 4 | | 3 | 4 | Best | 2.6193 | 2.3426 | 2.6193 | 2.6197 | tree | MinLeafSize: 29 | | | | | | | | | | MaxNumSplits: 52 | | | | | | | | | | NumVariablesToSample: 6 | | 4 | 4 | Accept | 4.1439 | 3.798 | 2.6193 | 2.6197 | svm | BoxConstraint: 0.010718 | | | | | | | | | | KernelScale: 1.7547 | | | | | | | | | | Epsilon: 182.6 | | 5 | 2 | Accept | 2.3998 | 8.4115 | 2.2082 | 2.6197 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.64294 | | | | | | | | | | MinLeafSize: 39 | | | | | | | | | | NumVariablesToSample: NaN | | 6 | 2 | Best | 2.2082 | 9.4573 | 2.2082 | 2.6197 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.033855 | | | | | | | | | | MinLeafSize: 6 | | | | | | | | | | NumVariablesToSample: NaN | | 7 | 2 | Accept | 4.1439 | 0.37564 | 2.2082 | 2.6197 | svm | BoxConstraint: 0.012677 | | | | | | | | | | KernelScale: 351.81 | | | | | | | | | | Epsilon: 140.99 | | 8 | 6 | Accept | 4.1439 | 1.1014 | 2.2082 | 2.6197 | svm | BoxConstraint: 37.191 | | | | | | | | | | KernelScale: 21.113 | | | | | | | | | | Epsilon: 33.874 | | 9 | 6 | Accept | 2.7394 | 1.8778 | 2.2082 | 2.6197 | svm | BoxConstraint: 0.057859 | | | | | | | | | | KernelScale: 448.87 | | | | | | | | | | Epsilon: 4.2169 | | 10 | 3 | Accept | 2.5987 | 6.4235 | 2.2082 | 2.4798 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.89898 | | | | | | | | | | MinLeafSize: 2 | | | | | | | | | | NumVariablesToSample: NaN | |===================================================================================================================================================| | Iter | Active | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 11 | 3 | Accept | 3.2336 | 6.93 | 2.2082 | 2.4798 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.56281 | | | | | | | | | | MinLeafSize: 123 | | | | | | | | | | NumVariablesToSample: NaN | | 12 | 3 | Accept | 2.682 | 6.4489 | 2.2082 | 2.4798 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 51 | | | | | | | | | | NumVariablesToSample: 2 | | 13 | 3 | Accept | 2.4795 | 0.40654 | 2.2082 | 2.4798 | tree | MinLeafSize: 6 | | | | | | | | | | MaxNumSplits: 32 | | | | | | | | | | NumVariablesToSample: 5 | | 14 | 5 | Accept | 4.1439 | 0.28349 | 2.2082 | 2.4798 | svm | BoxConstraint: 297.35 | | | | | | | | | | KernelScale: 0.87756 | | | | | | | | | | Epsilon: 0.043798 | | 15 | 5 | Accept | 2.845 | 0.3422 | 2.2082 | 2.4798 | svm | BoxConstraint: 0.0027083 | | | | | | | | | | KernelScale: 413.17 | | | | | | | | | | Epsilon: 0.13572 | | 16 | 5 | Accept | 2.7106 | 5.6397 | 2.2082 | 2.3735 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.74839 | | | | | | | | | | MinLeafSize: 88 | | | | | | | | | | NumVariablesToSample: NaN | | 17 | 3 | Accept | 6.0492 | 4.8396 | 2.2082 | 2.3735 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.0010498 | | | | | | | | | | MinLeafSize: 130 | | | | | | | | | | NumVariablesToSample: NaN | | 18 | 3 | Accept | 2.2932 | 5.4011 | 2.2082 | 2.3735 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.10542 | | | | | | | | | | MinLeafSize: 57 | | | | | | | | | | NumVariablesToSample: NaN | | 19 | 3 | Accept | 2.6686 | 0.22924 | 2.2082 | 2.3735 | tree | MinLeafSize: 5 | | | | | | | | | | MaxNumSplits: 7 | | | | | | | | | | NumVariablesToSample: 5 | | 20 | 6 | Accept | 4.1439 | 1.5528 | 2.2082 | 2.3735 | svm | BoxConstraint: 0.07294 | | | | | | | | | | KernelScale: 761.22 | | | | | | | | | | Epsilon: 31.544 | |===================================================================================================================================================| | Iter | Active | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 21 | 4 | Accept | 4.143 | 0.10249 | 2.2082 | 2.3735 | tree | MinLeafSize: 132 | | | | | | | | | | MaxNumSplits: 8 | | | | | | | | | | NumVariablesToSample: 5 | | 22 | 4 | Accept | 4.143 | 0.31889 | 2.2082 | 2.3735 | tree | MinLeafSize: 138 | | | | | | | | | | MaxNumSplits: 3 | | | | | | | | | | NumVariablesToSample: 7 | | 23 | 4 | Accept | 3.5024 | 0.16777 | 2.2082 | 2.3735 | tree | MinLeafSize: 83 | | | | | | | | | | MaxNumSplits: 41 | | | | | | | | | | NumVariablesToSample: 2 | | 24 | 2 | Accept | 4.1439 | 33.887 | 2.2082 | 2.3735 | svm | BoxConstraint: 0.15265 | | | | | | | | | | KernelScale: 1.4893 | | | | | | | | | | Epsilon: 0.44287 | | 25 | 2 | Accept | 2.3583 | 5.6469 | 2.2082 | 2.3735 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 2 | | | | | | | | | | NumVariablesToSample: 2 | | 26 | 2 | Accept | 4.1439 | 0.08045 | 2.2082 | 2.3735 | svm | BoxConstraint: 0.0050384 | | | | | | | | | | KernelScale: 0.18651 | | | | | | | | | | Epsilon: 11.818 | | 27 | 6 | Accept | 4.1439 | 0.11643 | 2.2082 | 2.3735 | svm | BoxConstraint: 0.19519 | | | | | | | | | | KernelScale: 0.48473 | | | | | | | | | | Epsilon: 0.02267 | | 28 | 6 | Accept | 2.6334 | 0.69581 | 2.2082 | 2.3735 | tree | MinLeafSize: 6 | | | | | | | | | | MaxNumSplits: 43 | | | | | | | | | | NumVariablesToSample: 2 | | 29 | 2 | Accept | 5.9862 | 5.4794 | 2.2082 | 2.3735 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.001143 | | | | | | | | | | MinLeafSize: 104 | | | | | | | | | | NumVariablesToSample: NaN | | 30 | 2 | Accept | 2.2456 | 7.9201 | 2.2082 | 2.3735 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 12 | | | | | | | | | | NumVariablesToSample: 7 | |===================================================================================================================================================| | Iter | Active | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 31 | 2 | Accept | 2.9745 | 7.6297 | 2.2082 | 2.3735 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.010155 | | | | | | | | | | MinLeafSize: 13 | | | | | | | | | | NumVariablesToSample: NaN | | 32 | 2 | Accept | 2.6819 | 6.0671 | 2.2082 | 2.3735 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 57 | | | | | | | | | | NumVariablesToSample: 5 | | 33 | 2 | Accept | 2.927 | 0.11096 | 2.2082 | 2.3735 | tree | MinLeafSize: 1 | | | | | | | | | | MaxNumSplits: 123 | | | | | | | | | | NumVariablesToSample: 2 | | 34 | 4 | Accept | 4.1439 | 0.11416 | 2.2082 | 2.3735 | svm | BoxConstraint: 2.1967 | | | | | | | | | | KernelScale: 0.02117 | | | | | | | | | | Epsilon: 0.20631 | | 35 | 4 | Accept | 2.9904 | 0.096707 | 2.2082 | 2.3735 | tree | MinLeafSize: 44 | | | | | | | | | | MaxNumSplits: 265 | | | | | | | | | | NumVariablesToSample: 2 | | 36 | 4 | Accept | 2.6513 | 0.10209 | 2.2082 | 2.3735 | tree | MinLeafSize: 1 | | | | | | | | | | MaxNumSplits: 90 | | | | | | | | | | NumVariablesToSample: 2 | | 37 | 4 | Accept | 2.2442 | 7.3117 | 2.2082 | 2.2083 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 1 | | | | | | | | | | NumVariablesToSample: 6 | | 38 | 4 | Accept | 2.345 | 5.3353 | 2.2082 | 2.2083 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 3 | | | | | | | | | | NumVariablesToSample: 2 | | 39 | 3 | Accept | 3.1314 | 4.9709 | 2.2082 | 2.2083 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 82 | | | | | | | | | | NumVariablesToSample: 5 | | 40 | 3 | Accept | 4.1439 | 0.076184 | 2.2082 | 2.2083 | svm | BoxConstraint: 488.75 | | | | | | | | | | KernelScale: 0.047261 | | | | | | | | | | Epsilon: 0.019147 | |===================================================================================================================================================| | Iter | Active | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 41 | 5 | Accept | 2.611 | 15.327 | 2.2082 | 2.2083 | svm | BoxConstraint: 0.0057698 | | | | | | | | | | KernelScale: 199.91 | | | | | | | | | | Epsilon: 1.094 | | 42 | 5 | Accept | 4.1439 | 0.11014 | 2.2082 | 2.2083 | svm | BoxConstraint: 347.06 | | | | | | | | | | KernelScale: 0.024995 | | | | | | | | | | Epsilon: 0.012891 | | 43 | 3 | Best | 2.1839 | 5.4291 | 2.1839 | 2.2083 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.079786 | | | | | | | | | | MinLeafSize: 16 | | | | | | | | | | NumVariablesToSample: NaN | | 44 | 3 | Accept | 2.9934 | 0.080707 | 2.1839 | 2.2083 | tree | MinLeafSize: 37 | | | | | | | | | | MaxNumSplits: 171 | | | | | | | | | | NumVariablesToSample: 4 | | 45 | 3 | Accept | 4.1439 | 0.090101 | 2.1839 | 2.2083 | svm | BoxConstraint: 0.24707 | | | | | | | | | | KernelScale: 0.0040563 | | | | | | | | | | Epsilon: 0.75695 | | 46 | 6 | Accept | 2.2144 | 5.1987 | 2.1839 | 2.1982 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.078839 | | | | | | | | | | MinLeafSize: 16 | | | | | | | | | | NumVariablesToSample: NaN | | 47 | 4 | Accept | 2.2877 | 5.9143 | 2.1839 | 2.1129 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 15 | | | | | | | | | | NumVariablesToSample: 5 | | 48 | 4 | Accept | 3.0763 | 0.13281 | 2.1839 | 2.1129 | tree | MinLeafSize: 12 | | | | | | | | | | MaxNumSplits: 2 | | | | | | | | | | NumVariablesToSample: 3 | | 49 | 4 | Accept | 4.1439 | 1.3244 | 2.1839 | 2.1129 | svm | BoxConstraint: 6.6689 | | | | | | | | | | KernelScale: 0.048705 | | | | | | | | | | Epsilon: 59.545 | | 50 | 3 | Accept | 4.1439 | 30.675 | 2.1839 | 2.1984 | svm | BoxConstraint: 13.655 | | | | | | | | | | KernelScale: 4.3086 | | | | | | | | | | Epsilon: 6.9116 | |===================================================================================================================================================| | Iter | Active | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 51 | 3 | Accept | 2.2728 | 5.7106 | 2.1839 | 2.1984 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 14 | | | | | | | | | | NumVariablesToSample: 5 | | 52 | 6 | Accept | 2.4156 | 4.7264 | 2.1839 | 2.1984 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 24 | | | | | | | | | | NumVariablesToSample: 3 | | 53 | 4 | Accept | 4.1439 | 0.07497 | 2.1839 | 2.1984 | svm | BoxConstraint: 424.87 | | | | | | | | | | KernelScale: 0.41352 | | | | | | | | | | Epsilon: 0.74479 | | 54 | 4 | Accept | 2.3527 | 5.0415 | 2.1839 | 2.1984 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.62721 | | | | | | | | | | MinLeafSize: 3 | | | | | | | | | | NumVariablesToSample: NaN | | 55 | 4 | Accept | 2.5975 | 0.086879 | 2.1839 | 2.1984 | tree | MinLeafSize: 2 | | | | | | | | | | MaxNumSplits: 12 | | | | | | | | | | NumVariablesToSample: 6 | | 56 | 3 | Accept | 4.1439 | 30.921 | 2.1839 | 2.1983 | svm | BoxConstraint: 0.0044643 | | | | | | | | | | KernelScale: 4.2576 | | | | | | | | | | Epsilon: 0.066941 | | 57 | 3 | Accept | 2.2488 | 6.5278 | 2.1839 | 2.1983 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 4 | | | | | | | | | | NumVariablesToSample: 6 | | 58 | 5 | Accept | 2.2375 | 6.3071 | 2.1839 | 2.1982 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 4 | | | | | | | | | | NumVariablesToSample: 6 | | 59 | 5 | Accept | 2.2145 | 5.1044 | 2.1839 | 2.1982 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.13809 | | | | | | | | | | MinLeafSize: 5 | | | | | | | | | | NumVariablesToSample: NaN | | 60 | 2 | Accept | 2.2771 | 5.7956 | 2.1839 | 2.1953 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 2 | | | | | | | | | | NumVariablesToSample: 4 | |===================================================================================================================================================| | Iter | Active | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 61 | 2 | Accept | 2.4755 | 4.7265 | 2.1839 | 2.1953 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 5 | | | | | | | | | | NumVariablesToSample: 1 | | 62 | 2 | Accept | 2.6456 | 0.082657 | 2.1839 | 2.1953 | tree | MinLeafSize: 2 | | | | | | | | | | MaxNumSplits: 36 | | | | | | | | | | NumVariablesToSample: 4 | | 63 | 2 | Accept | 2.5294 | 5.4057 | 2.1839 | 2.1953 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 35 | | | | | | | | | | NumVariablesToSample: 5 | | 64 | 6 | Accept | 2.3409 | 5.5648 | 2.1839 | 2.0591 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 25 | | | | | | | | | | NumVariablesToSample: 6 | | 65 | 2 | Accept | 2.3209 | 7.4037 | 2.1839 | 2.0591 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.016875 | | | | | | | | | | MinLeafSize: 1 | | | | | | | | | | NumVariablesToSample: NaN | | 66 | 2 | Accept | 2.5782 | 5.5342 | 2.1839 | 2.0591 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.015531 | | | | | | | | | | MinLeafSize: 76 | | | | | | | | | | NumVariablesToSample: NaN | | 67 | 2 | Accept | 2.2537 | 7.2619 | 2.1839 | 2.0591 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 6 | | | | | | | | | | NumVariablesToSample: 7 | | 68 | 2 | Accept | 4.1426 | 4.7455 | 2.1839 | 2.0591 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 134 | | | | | | | | | | NumVariablesToSample: 2 | | 69 | 2 | Accept | 2.9366 | 0.094426 | 2.1839 | 2.0591 | tree | MinLeafSize: 8 | | | | | | | | | | MaxNumSplits: 37 | | | | | | | | | | NumVariablesToSample: 1 | | 70 | 6 | Accept | 2.2338 | 5.1862 | 2.1839 | 2.1934 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.17516 | | | | | | | | | | MinLeafSize: 9 | | | | | | | | | | NumVariablesToSample: NaN | |===================================================================================================================================================| | Iter | Active | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 71 | 3 | Accept | 4.143 | 4.4939 | 2.1839 | 2.1968 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.038144 | | | | | | | | | | MinLeafSize: 142 | | | | | | | | | | NumVariablesToSample: NaN | | 72 | 3 | Accept | 4.1439 | 0.076138 | 2.1839 | 2.1968 | svm | BoxConstraint: 131.74 | | | | | | | | | | KernelScale: 0.0031145 | | | | | | | | | | Epsilon: 0.028465 | | 73 | 3 | Accept | 4.143 | 0.074774 | 2.1839 | 2.1968 | tree | MinLeafSize: 156 | | | | | | | | | | MaxNumSplits: 1 | | | | | | | | | | NumVariablesToSample: 5 | | 74 | 3 | Accept | 2.3197 | 5.1527 | 2.1839 | 2.1968 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 9 | | | | | | | | | | NumVariablesToSample: 3 | | 75 | 6 | Accept | 2.5309 | 4.7886 | 2.1839 | 2.1969 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.97421 | | | | | | | | | | MinLeafSize: 13 | | | | | | | | | | NumVariablesToSample: NaN | | 76 | 3 | Accept | 2.2935 | 5.3774 | 2.1839 | 2.1983 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.16149 | | | | | | | | | | MinLeafSize: 30 | | | | | | | | | | NumVariablesToSample: NaN | | 77 | 3 | Accept | 2.3649 | 4.9029 | 2.1839 | 2.1983 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 2 | | | | | | | | | | NumVariablesToSample: 2 | | 78 | 3 | Accept | 3.3541 | 0.065977 | 2.1839 | 2.1983 | tree | MinLeafSize: 79 | | | | | | | | | | MaxNumSplits: 65 | | | | | | | | | | NumVariablesToSample: 3 | | 79 | 3 | Accept | 2.3592 | 5.0572 | 2.1839 | 2.1983 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 1 | | | | | | | | | | NumVariablesToSample: 2 | | 80 | 6 | Accept | 2.4009 | 4.5836 | 2.1839 | 2.1983 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 18 | | | | | | | | | | NumVariablesToSample: 2 | |===================================================================================================================================================| | Iter | Active | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 81 | 2 | Accept | 10.894 | 31.052 | 2.1839 | 2.1983 | svm | BoxConstraint: 0.05924 | | | | | | | | | | KernelScale: 16.477 | | | | | | | | | | Epsilon: 1.204 | | 82 | 2 | Accept | 2.216 | 5.8077 | 2.1839 | 2.1983 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.038621 | | | | | | | | | | MinLeafSize: 2 | | | | | | | | | | NumVariablesToSample: NaN | | 83 | 2 | Accept | 2.2547 | 5.6201 | 2.1839 | 2.1983 | ensemble | Method: Bag | | | | | | | | | | LearnRate: NaN | | | | | | | | | | MinLeafSize: 4 | | | | | | | | | | NumVariablesToSample: 5 | | 84 | 2 | Accept | 4.1439 | 0.11346 | 2.1839 | 2.1983 | svm | BoxConstraint: 230.13 | | | | | | | | | | KernelScale: 15.715 | | | | | | | | | | Epsilon: 425.18 | | 85 | 2 | Accept | 4.1439 | 0.10597 | 2.1839 | 2.1983 | svm | BoxConstraint: 10.758 | | | | | | | | | | KernelScale: 0.020507 | | | | | | | | | | Epsilon: 4.9755 | | 86 | 6 | Accept | 2.219 | 6.1221 | 2.1839 | 2.1981 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.038658 | | | | | | | | | | MinLeafSize: 2 | | | | | | | | | | NumVariablesToSample: NaN | | 87 | 2 | Accept | 2.8447 | 0.17007 | 2.1839 | 2.1981 | svm | BoxConstraint: 0.013729 | | | | | | | | | | KernelScale: 535.02 | | | | | | | | | | Epsilon: 2.1063 | | 88 | 2 | Accept | 4.1439 | 0.079667 | 2.1839 | 2.1981 | svm | BoxConstraint: 0.32731 | | | | | | | | | | KernelScale: 22.615 | | | | | | | | | | Epsilon: 41.604 | | 89 | 2 | Accept | 2.2928 | 4.9488 | 2.1839 | 2.1981 | ensemble | Method: LSBoost | | | | | | | | | | LearnRate: 0.26144 | | | | | | | | | | MinLeafSize: 33 | | | | | | | | | | NumVariablesToSample: NaN | | 90 | 2 | Accept | 2.4525 | 0.12704 | 2.1839 | 2.1981 | tree | MinLeafSize: 4 | | | | | | | | | | MaxNumSplits: 92 | | | | | | | | | | NumVariablesToSample: 7 | |===================================================================================================================================================| | Iter | Active | Eval | log(1 + valLoss) | Time for training | Observed min | Estimated min | Learner | Hyperparameter: Value | | | workers | result | | & validation (sec)| log(1 + valLoss) | log(1 + valLoss) | | | |===================================================================================================================================================| | 91 | 2 | Accept | 4.1439 | 0.093014 | 2.1839 | 2.1981 | svm | BoxConstraint: 0.0021134 | | | | | | | | | | KernelScale: 0.001228 | | | | | | | | | | Epsilon: 6.4785 | __________________________________________________________ Optimization completed. Total iterations: 91 Total elapsed time: 235.4082 seconds Total time for training and validation: 426.1606 seconds Best observed learner is an ensemble model with: Method: LSBoost LearnRate: 0.079786 MinLeafSize: 16 NumVariablesToSample: NaN Observed log(1 + valLoss): 2.1839 Time for training and validation: 5.4291 seconds Best estimated learner (returned model) is an ensemble model with: Method: LSBoost LearnRate: 0.079786 MinLeafSize: 16 NumVariablesToSample: NaN Estimated log(1 + valLoss): 2.1981 Estimated time for training and validation: 5.3328 seconds Documentation for fitrauto display
Последняя модель, возвращенная fitrauto соответствует лучшему предполагаемому ученику. Перед возвращением модели функция переобучает её, используя все данные обучения (carsTrain), перечисленные Learner тип (или модель) и отображаемые значения гиперпараметров.
Создание простой модели
Создание простой модели линейной регрессии linearMdl с помощью fitlm функция.
linearMdl = fitlm(carsTrain);
Хотя linearMdl объект не имеет точно таких же свойств и методов, как autoMdl , можно использовать обе модели для прогнозирования значений ответа для новых данных с помощью predict объектная функция.
Сравнение производительности тестового набора моделей
Сравните производительность linearMdl и autoMdl модели в наборе тестовых данных. Для каждой модели вычислите среднеквадратичную ошибку (MSE) тестового набора. Меньшие значения MSE указывают на лучшую производительность.
ypred = predict(linearMdl,carsTest);
linearMSE = mean((carsTest.MPG-ypred).^2,'omitnan')linearMSE = 11.0981
autoMSE = loss(autoMdl,carsTest,'MPG')autoMSE = 8.8024
autoMdl модель, по-видимому, превосходит linearMdl модель.
В зависимости от размера ваших данных и указанного количества учащихся, fitrauto может занять некоторое время, чтобы бежать. При наличии лицензии Parallel Computing Toolbox можно ускорить вычисления путем параллельного выполнения оптимизации. Для этого укажите 'HyperparameterOptimizationOptions',struct('UseParallel',true). Для управления другими аспектами оптимизации в структуру можно включить другие поля. Посмотрите HyperparameterOptimizationOptions.
Если вы не уверены, какие модели лучше всего подходят для вашего набора данных, вы можете также использовать приложение «Обучающийся регрессии». С помощью приложения вы можете выполнить гиперпараметрическую настройку для различных моделей и выбрать оптимальную модель, которая работает лучше всего. Несмотря на то, что перед настройкой гиперпараметров модели необходимо выбрать определенную модель, функция «Обучение регрессии» обеспечивает большую гибкость при выборе оптимизируемых гиперпараметров и установке значений гиперпараметров. Приложение также позволяет обучать различные модели линейной регрессии (см. Модели линейной регрессии). Однако параллельно оптимизировать нельзя, выберите 'linear' или 'kernel' учащиеся или укажите веса наблюдений в приложении. Дополнительные сведения см. в разделе Оптимизация гиперпараметров в приложении для учащихся с регрессией.
Если известно, какие модели могут соответствовать данным, можно также использовать соответствующие функции аппроксимации модели и указать 'OptimizeHyperparameters' аргумент пары имя-значение для настройки гиперпараметров. Можно сравнить результаты по моделям, чтобы выбрать лучшую регрессионную модель. Пример этого процесса, применяемого к классификационным моделям, см. в разделе Переход к автоматизации выбора модели с использованием байесовской оптимизации.
fitrensemble | fitrgp | fitrkernel | fitrlinear | fitrsvm | fitrtree